I've been reading my analysis notes. When they define the sequences of functions and the pointwise and uniform convergence, it says that it has to converge to a function $f$. Then, they define the series of functions and the statements are almost analogue to the sequences of functions, but here it says: a series of functions $\sum{f_n}$ converges pointwise on the interval $I$ if the sequence of partial sums converge pointwise. The same for the uniform convergence. After that, it's like they always say "this series converges uniformly here" but they don't say where, they don't say "it converges here to this function".
Why they do this? The natural way to see it invites to say that something converges to something. It's not necessary to check the uniform convergence of a function to know where it actually converges?
Thanks for taking the time.